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      第一周习题
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        <p>1.<br><figure class="highlight matlab"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br></pre></td><td class="code"><pre><span class="line">&gt;&gt; randintr(<span class="number">4</span>,<span class="number">5</span>)</span><br><span class="line"></span><br><span class="line"><span class="built_in">ans</span> =</span><br><span class="line"></span><br><span class="line">     <span class="number">6</span>     <span class="number">3</span>     <span class="number">9</span>     <span class="number">9</span>    <span class="number">-1</span></span><br><span class="line">     <span class="number">8</span>    <span class="number">-8</span>     <span class="number">9</span>     <span class="number">0</span>     <span class="number">8</span></span><br><span class="line">    <span class="number">-7</span>    <span class="number">-4</span>    <span class="number">-7</span>     <span class="number">6</span>     <span class="number">6</span></span><br><span class="line">     <span class="number">8</span>     <span class="number">1</span>     <span class="number">9</span>    <span class="number">-7</span>     <span class="number">9</span></span><br><span class="line"></span><br><span class="line">&gt;&gt; A=<span class="built_in">ans</span></span><br><span class="line"></span><br><span class="line">A =</span><br><span class="line"></span><br><span class="line">     <span class="number">6</span>     <span class="number">3</span>     <span class="number">9</span>     <span class="number">9</span>    <span class="number">-1</span></span><br><span class="line">     <span class="number">8</span>    <span class="number">-8</span>     <span class="number">9</span>     <span class="number">0</span>     <span class="number">8</span></span><br><span class="line">    <span class="number">-7</span>    <span class="number">-4</span>    <span class="number">-7</span>     <span class="number">6</span>     <span class="number">6</span></span><br><span class="line">     <span class="number">8</span>     <span class="number">1</span>     <span class="number">9</span>    <span class="number">-7</span>     <span class="number">9</span></span><br><span class="line"></span><br><span class="line">&gt;&gt; ref1(A)</span><br><span class="line"></span><br><span class="line"><span class="built_in">ans</span> =</span><br><span class="line"></span><br><span class="line">    <span class="number">8.0000</span>   <span class="number">-8.0000</span>    <span class="number">9.0000</span>         <span class="number">0</span>    <span class="number">8.0000</span></span><br><span class="line">         <span class="number">0</span>  <span class="number">-11.0000</span>    <span class="number">0.8750</span>    <span class="number">6.0000</span>   <span class="number">13.0000</span></span><br><span class="line">         <span class="number">0</span>         <span class="number">0</span>    <span class="number">2.9659</span>   <span class="number">13.9091</span>    <span class="number">3.6364</span></span><br><span class="line">         <span class="number">0</span>         <span class="number">0</span>         <span class="number">0</span>   <span class="number">-5.4483</span>   <span class="number">10.7586</span></span><br><span class="line"></span><br><span class="line">&gt;&gt; rref(A)</span><br><span class="line"></span><br><span class="line"><span class="built_in">ans</span> =</span><br><span class="line"></span><br><span class="line">    <span class="number">1.0000</span>         <span class="number">0</span>         <span class="number">0</span>         <span class="number">0</span>  <span class="number">-12.2222</span></span><br><span class="line">         <span class="number">0</span>    <span class="number">1.0000</span>         <span class="number">0</span>         <span class="number">0</span>   <span class="number">-1.4248</span></span><br><span class="line">         <span class="number">0</span>         <span class="number">0</span>    <span class="number">1.0000</span>         <span class="number">0</span>   <span class="number">10.4866</span></span><br><span class="line">         <span class="number">0</span>         <span class="number">0</span>         <span class="number">0</span>    <span class="number">1.0000</span>   <span class="number">-1.9747</span></span><br><span class="line"></span><br><span class="line">&gt;&gt; A=randintr(<span class="number">5</span>,<span class="number">6</span>,<span class="number">20</span>)</span><br><span class="line"></span><br><span class="line">A =</span><br><span class="line"></span><br><span class="line">     <span class="number">6</span>    <span class="number">11</span>     <span class="number">8</span>    <span class="number">13</span>    <span class="number">-3</span>     <span class="number">0</span></span><br><span class="line">   <span class="number">-19</span>    <span class="number">10</span>   <span class="number">-19</span>     <span class="number">8</span>    <span class="number">-5</span>    <span class="number">-2</span></span><br><span class="line">    <span class="number">14</span>    <span class="number">-4</span>    <span class="number">-9</span>    <span class="number">-7</span>    <span class="number">11</span>     <span class="number">6</span></span><br><span class="line">    <span class="number">18</span>     <span class="number">6</span>   <span class="number">-19</span>    <span class="number">18</span>    <span class="number">12</span>     <span class="number">9</span></span><br><span class="line">     <span class="number">7</span>   <span class="number">-13</span>   <span class="number">-17</span>   <span class="number">-19</span>   <span class="number">-13</span>    <span class="number">10</span></span><br><span class="line"></span><br><span class="line">&gt;&gt; rref(A)</span><br><span class="line"></span><br><span class="line"><span class="built_in">ans</span> =</span><br><span class="line"></span><br><span class="line">    <span class="number">1.0000</span>         <span class="number">0</span>         <span class="number">0</span>         <span class="number">0</span>         <span class="number">0</span>    <span class="number">0.3738</span></span><br><span class="line">         <span class="number">0</span>    <span class="number">1.0000</span>         <span class="number">0</span>         <span class="number">0</span>         <span class="number">0</span>   <span class="number">-0.0423</span></span><br><span class="line">         <span class="number">0</span>         <span class="number">0</span>    <span class="number">1.0000</span>         <span class="number">0</span>         <span class="number">0</span>   <span class="number">-0.2548</span></span><br><span class="line">         <span class="number">0</span>         <span class="number">0</span>         <span class="number">0</span>    <span class="number">1.0000</span>         <span class="number">0</span>   <span class="number">-0.0182</span></span><br><span class="line">         <span class="number">0</span>         <span class="number">0</span>         <span class="number">0</span>         <span class="number">0</span>    <span class="number">1.0000</span>   <span class="number">-0.1658</span></span><br></pre></td></tr></table></figure></p>
<ol>
<li><p>解方程组</p>
<figure class="highlight matlab"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br></pre></td><td class="code"><pre><span class="line">&gt;&gt; A = [ <span class="number">3</span> <span class="number">-2</span> <span class="number">-5</span> <span class="number">1</span>; <span class="number">2</span> <span class="number">-3</span> <span class="number">1</span> <span class="number">5</span>;<span class="number">1</span> <span class="number">2</span> <span class="number">0</span> <span class="number">-4</span>; <span class="number">1</span> <span class="number">-1</span> <span class="number">-4</span> <span class="number">9</span>]</span><br><span class="line"></span><br><span class="line">A =</span><br><span class="line"></span><br><span class="line">       <span class="number">3</span>             <span class="number">-2</span>             <span class="number">-5</span>              <span class="number">1</span></span><br><span class="line">       <span class="number">2</span>             <span class="number">-3</span>              <span class="number">1</span>              <span class="number">5</span></span><br><span class="line">       <span class="number">1</span>              <span class="number">2</span>              <span class="number">0</span>             <span class="number">-4</span></span><br><span class="line">       <span class="number">1</span>             <span class="number">-1</span>             <span class="number">-4</span>              <span class="number">9</span></span><br><span class="line"></span><br><span class="line">&gt;&gt; b = [<span class="number">3</span>; <span class="number">-3</span>; <span class="number">-3</span>; <span class="number">22</span>]</span><br><span class="line"></span><br><span class="line">b =</span><br><span class="line"></span><br><span class="line">       <span class="number">3</span></span><br><span class="line">      <span class="number">-3</span></span><br><span class="line">      <span class="number">-3</span></span><br><span class="line">      <span class="number">22</span></span><br><span class="line"></span><br><span class="line">&gt;&gt; [U,ip]=rref([A,b])</span><br><span class="line"></span><br><span class="line">U =</span><br><span class="line"></span><br><span class="line">       <span class="number">1</span>              <span class="number">0</span>              <span class="number">0</span>              <span class="number">0</span>             <span class="number">-1</span></span><br><span class="line">       <span class="number">0</span>              <span class="number">1</span>              <span class="number">0</span>              <span class="number">0</span>              <span class="number">3</span></span><br><span class="line">       <span class="number">0</span>              <span class="number">0</span>              <span class="number">1</span>              <span class="number">0</span>             <span class="number">-2</span></span><br><span class="line">       <span class="number">0</span>              <span class="number">0</span>              <span class="number">0</span>              <span class="number">1</span>              <span class="number">2</span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line">ip =</span><br><span class="line"></span><br><span class="line">       <span class="number">1</span>              <span class="number">2</span>              <span class="number">3</span>              <span class="number">4</span></span><br></pre></td></tr></table></figure>
</li>
<li><p>交通流量</p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br></pre></td><td class="code"><pre><span class="line">&gt;&gt; A = [0 -1 0 0 1; 0 0 0 1 -1; 1 1 0 0 0;0 0 1 1 0; -1 0 1 0 0;]</span><br><span class="line"></span><br><span class="line">A =</span><br><span class="line"></span><br><span class="line">       0             -1              0              0              1</span><br><span class="line">       0              0              0              1             -1</span><br><span class="line">       1              1              0              0              0</span><br><span class="line">       0              0              1              1              0</span><br><span class="line">      -1              0              1              0              0</span><br><span class="line"></span><br><span class="line">&gt;&gt; b = [300; -100; 300; 700; 200]</span><br><span class="line"></span><br><span class="line">b =</span><br><span class="line"></span><br><span class="line">     300</span><br><span class="line">    -100</span><br><span class="line">     300</span><br><span class="line">     700</span><br><span class="line">     200</span><br><span class="line"></span><br><span class="line">&gt;&gt; [U,ip] = rref([A,b])</span><br><span class="line"></span><br><span class="line">U =</span><br><span class="line"></span><br><span class="line">       1              0              0              0              1            600</span><br><span class="line">       0              1              0              0             -1           -300</span><br><span class="line">       0              0              1              0              1            800</span><br><span class="line">       0              0              0              1             -1           -100</span><br><span class="line">       0              0              0              0              0              0</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">ip =</span><br><span class="line"></span><br><span class="line">       1              2              3              4</span><br></pre></td></tr></table></figure>
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<li><p>解三次多项式</p>
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